Newton's Second Law for an Extended ObjectThe utility of Newton's second law for the description of the motion of extended objects is the key to its general practical usefulness. The motion of any real object may involve rotations as well as linear motion, but the motion of the center of mass of the object can be described by an application of Newton's second law in the following form:
If you know the net force exerted upon an object, you can predict the motion of its center of mass, even though it may be executing rotation or other internal motions. The standard visualization examples for this application are:

Index Newton's 2nd Law Concepts  

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Newton's Second Law for a System of ParticlesThe form of Newton's second law for a system of particles will be developed with the understanding that the result will apply to any extended object where the particles are in face connected to each other. The center of mass of a system of particles can be determined from their masses and locations. This center of mass can be located by a position vector: The velocity of the center of mass can be obtained by taking the derivative of the position vector. Rearranging this shows that the total momentum of the system of particles is just the total mass times the velocity of the center of mass. Then taking the derivative of this expression gives where F_{i} is the vector force on the i^{th} particle. This can be rearranged to the form Since nothing we have done addressed whether the particles are connected or not, this result generally applies to a system of discrete particles or to an extended object consisting of connected mass elements. 
Index Newton's 2nd Law Concepts  

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